Question

A circle has a circumference of C inches and an area of A square inches. inches. fC = 2/5 * A what is the diameter of the circle?

0.4 in.
0.8 in
2.5 in
10in

Answer 1

`\it R=circle's \ radius;\ \ D=diameter;\ \ D=2R\\ \\ \mathcal{C}=2\pi R\\ \\ \mathcal{A}=\pi R^2\\ \\ \mathcal{C}=(2)/(5)\cdot\mathcal{A} \Rightarrow 2\pi R=(2)/(5)\pi R^2|_{\cdot(5)/(2)} \Rightarrow 5\pi R=\pi R^2|_(:(\pi R)) \Rightarrow 5=R|_(\cdot2) \Rightarrow 10=2R\\ \\ But,\ 2R=D,\ so\ \ D=10\ in`